How to create an AI snake for a video game?
A relatively simple option which uses AI techniques that are 'traditional' for adversarial games (and which is therefore less of a 'research project' than the use of Machine Learning) is Minimax.

The ingredients for this are:


A list of all the actions that a snake can immediately perform from its current position.
A measure of quality (a.k.a. 'fitness') for the resulting world state.


Traditionally specified for two opponents, the minimax algorithm looks a specified number of moves ahead (alternating between opponents at each turn) and attempts to find the world state that maximizes the quality measure for one opponent whilst minimizing it for the other.

An extension of the two-player algorithm to n opponents (as seemingly required by the OP) is given in this paper.